This is strange.
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Proof of overlapping universes?
- pt
On Friday, September 21, 2018 at 11:38:06 PM UTC-5, Bruce wrote:
>
> From: Brent Meeker <[email protected] <javascript:>>
>
>
> On Friday, September 21, 2018 at 12:11:01 AM UTC-5, Bruce Kellett wrote:
>>
>> Adrian Kent (arXiv:1408.1944) makes some interesting comments about the
>> recent argument by Sebens and Carroll (arXiv:1405.7577) that probability in
>> MWI can be understood in terms of self-locating uncertainty -- when all
>> outcomes of a measurement are realized in unitary quantum mechanics,
>> probabilities might arise because one is does not know in which branch of
>> the universal wave function one is located. Kent points out that this
>> raises questions about how branches are formed in unitary quantum mechanics.
>>
>> The usual Everettian argument is that when one measures a state with two
>> possible outcomes, say a spin-1/2 particle, unitary evolution takes the
>> states representing the apparatus, observer, and environment to a FAPP
>> orthogonal set of states branched according to each of the possible
>> measurement results. Schematically, one writes the interaction with
>>
>> |psi> = (|+> + |->)/sqrt(2)
>>
>> as |psi>|O>, where O is the "ready" state of the observer (including
>> apparatus and environment). Thus:
>>
>> (|+> + |->)|O>
>> At this point there is just one observer who has not become entangled
>> with the apparatus or the rest of the environment. To take this to the next
>> stage, Kent points out that we use the distribution law of algebra to
>> eliminate the above brackets, and write
>>
>
> It seems that you are treating this mathematical rewriting as a physical
> process. Why insert it between
> (|+> + |->)|O> and |+>|O+> + |->|O-> and create the appearance of a
> problem?
>
>
> There is a lacuna in the physical narrative at this point. Each component
> of the superposition acts on the apparatus/observer in the same 'ready'
> state in order to get |O+> as different from |O->. This differentiation
> must take place before decoherence acts to diagonalize the density matrix.
> Otherwise all terms in the density matrix would be the same and there would
> be no distinction between outcomes. You can't just paper over this
> explanatory gap by calling it a mathematical rewriting.
>
> Bruce
>
>
>
>
> Brent
>
>
> |+>|O> + |->|O> (O is uncertain which result he will see)
>>
>> which, by unitary evolution, becomes entangled with the rest of the wave
>> function:
>>
>> |+>|O+> + |->|O-> ( O has a definite result>
>>
>> representing observers who record '+' or '-' results, respectively.
>> Before the last step, the observer does not know which branch he is on,
>> hence the self-locating uncertainty that is presumed to be the origin of
>> quantum probabilities.
>>
>> But Kent points out that there is a problem with this -- in the line in
>> which O is uncertain, the observer has already split: there is a copy on
>> each branch of the wave function, even though the observer has not yet
>> interacted with the apparatus or the environment, so what caused the
>> observer to split and appear on both branches in this way? We have used the
>> distribution law of algebra to expand the brackets in such as way as to
>> naively indicate that such a split has taken place. But how does this
>> actually happen, physically? Above we are just talking about equations --
>> these have to be related to the physics in some unambiguous way.
>>
>> Kent comments on the problem that this causes for the Sebens and Carroll
>> idea of probability as self-locating uncertainty. But it would seem that
>> the problem is deeper than this. We commonly divide the Hilbert space into
>> the tensor product of subspaces representing the apparatus and the
>> environment, as well as the observer. Then unitary evolution is supposed to
>> act on each component of this product space so that, ultimately,
>> decoherence renders the branches FAPP orthogonal, and we can then talk of
>> separate "worlds". But there is no reason to suppose that this division
>> into convenient classical components corresponds to any actual
>> factorization of the quantum Hilbert space -- there is no clear separation
>> into apparatus-observer-environment, so it is reasonable to call them all
>> the one thing, as I have done above.
>>
>> Kent comments on this situation as follows:
>> "...these are just statements about ink on paper. To translate them into
>> statements about one or more observers, who are uncertain about some
>> relevant fact about their location on branches, requires some principled
>> general account of how we start from the universal wave function and derive
>> an ontology that includes (at least) observers and branches.....and
>> observers must be split into copies before they observe the relevant
>> event." Kent sees several problems with any such approach to understanding
>> the above, apparently simple, mathematical relations.
>>
>> His conclusion is: "Fifty-seven years of sometimes careful work on trying
>> to make scientific sense of Everettian quantum theory ought, surely, to
>> have persuaded the theoretical physics community that one cannot make
>> useful progress this way. Whatever one thinks of the scientific status of
>> many worlds quantum theory, one cannot reasonably, at this point, think it
>> is so obvious how to translate equations into statements about a
>> many-worlds reality that arguments and explanations are redundant."
>>
>> And again: "Moreover, it is worth underlining again here that, if we
>> *were* able to find reasonably natural postulates that respected
>> physical symmetries and defined an objective branching structure for the
>> universal wave function, it would be superfluous to postulate many
>> independent real worlds. It would be simpler and more natural to postulate
>> that precisely one of the branches is randomly chosen (using the Born
>> wright distribution) and realized in nature."
>>
>> That idea would certainly overcome the problem of the apparent need for
>> apparatus, observers, and the environment to split *before* there is any
>> interaction -- one potential branch is randomly chosen, and then that
>> branch develops in the standard way. In reality there would be no splitting
>> -- just a stochastic process.
>>
>> Bruce
>>
>
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